Multiplying fractions and whole numbers

What is a whole number

You’ve encountered lots of whole numbers before now. Whole numbers are numbers that aren’t fractions—they are integers. For example, 2,122, 122,12, and 505050 would all be whole numbers.

On the other hand, numbers that aren’t whole numbers would look something like 1.251.251.25 or 45\frac{4}{5}54​. Although a fraction is a rational number, it is not a whole number. Knowing the difference will be important in this lesson

How to multiply fractions with whole numbers

When you’re given a question that requires you to deal with multiplying fractions with whole numbers, there’s 444 main steps you’ll have to carry out.

Firstly, rewrite the question so that the whole number is turned into a fraction. As you probably already know, when you have a whole number, turning it into a fraction just requires you to put it over 111. So for example, if you wanted to convert 888 into a fraction, it’ll be rewritten as 81\frac{8}{1}18​.

Secondly, multiply the two numerators in the two respective fractions. This just means taking the two numbers on top of each of the fractions and then multiplying them with one another.

For the third step, do the same as step two but now you’re using the two numbers in the denominators in the fractions. You’ll end up with a new fraction after doing steps two and three!

Lastly, you’ll just have to simplify the fraction you’ve gotten after solving the problem. You have to show your answer in the lowest terms possible, or you may get marks deducted for not having completely finished the question. Let’s take a look at some examples and put the four steps into use to help you with multiplying fractions and whole numbers.

Practice problems

Question 1:

Calculate

2×152 \times \frac{1}{5}2×51​

Solution:

First, we can express 222 as a fraction:

21\frac{2}{1}12​

Our question will then be converted to something that looks like this:

21×15\frac{2}{1} \times \frac{1}{5}12​×51​

We multiply these fractions, first tackling the top numbers (2×12 \times 12×1) and then doing the bottom ones (1×51 \times 51×5). Then we’ll get our final number, which is a new fraction.

21×15=25\frac{2}{1} \times \frac{1}{5} = \frac{2}{5}12​×51​=52​

Since 25\frac{2}{5}52​ is already the most simplified form of the fraction, this will be your final answer.

Simplified form of the fraction

Question 2:

A pizza had 121212 slices, and 34\frac{3}{4}43​ of it was eaten in a party. How many slices of pizza were eaten during the party?

Solution:

There were 121212 slices and 34\frac{3}{4}43​ were eaten. So we multiply 121212 and 34\frac{3}{4}43​ to get the answer. Let’s express 121212 as a fraction.

121×34\frac{12}{1} \times \frac{3}{4}112​×43​

Before doing multiplication, we can simplify the question first and get this:

Don't just watch, practice makes perfect.

Multiplying fractions and whole numbers

We learned previously that whole numbers can be written We learned previously that whole numbers can be written as fractions with 1 as the denominator and the whole number as the numerator. To make the calculation easier, we can first make the whole numbers into fraction when we multiply whole numbers with fractions. By doing so, we turn the questions into multiplying fractions only.